# Multistage Growth Dividend Discount Model

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Multiple Stage Dividend Discount Models better reflect reality than models assuming a constant growth rate and dividend policy into perpetuity. The benefit is fairly obvious: Firms change with time, and assuming a constant growth rate and dividend policy ignores that reality. A multiple stage model where you can change and modify growth rates and dividend payouts can be adjusted to your firm. You can pick any growth rates and dividend policies you need to value the shares based on dividend payout.

You need a few preparation calculations to compute the model. The first piece of information you need to determine is the length of the holding period, which determines the amount of time you are forecasting dividend growth.

The second requirement is dividends for the duration of the period which you are calculating. The constant growth dividend discount model offers no rate flexibility since it uses a single rate in perpetuity. A Multiple Stage Dividend Discount Model delivers substantial flexibility in choosing your growth rates. In the constant growth method, you pick the growth rate once and it calculates the future in perpetuity. In multiple stage dividend discount models, you set the dividend value manually for each year during the entire process. If you factor your dividend growth into your dividend selection, this sets the growth rate manually for each year.

For example, let’s say you anticipate an accelerating growth rate starting with a $2.00 dividend. In the first year you anticipate the dividend will grow by 10%, accelerating to 14% over 5 years. Your calculations for those 4 years of dividends can appear like this.

Your dividend for the first year would be: 2.00*(1+.10) = 2.20.

Your dividend for the second year would be: 2.20*(1+.11) = 2.44.

Your dividend for the third year would be: 2.44*(1+.12) = 2.74.

Your dividend for the fourth year would be: 2.74*(1+.13) = 3.10.

Your dividend for the fifth year, your final year, would be: 3.10*(1+.14) = 3.53.

Note that the final year’s dividend becomes very important later on.

The previous example is for an accelerating dividend rate. By substituting any percentage for growth in decimals you can emulate any number of scenarios. A decreasing series of growth rates indicates a slowdown in growth over time. You could interpolate, accelerate, or decelerate rate declines. You have a fairly large amount of flexibility.

If you use analyst service providers to acquire dividend forecasts, you can insert their dividend price projections directly into the model on a year by year basis without calculating growth. Alternatively, you can calculate growth if they give you year by year growth rates and a base dividend and insert those into the model.

After you’ve acquired or created your dividend projects you can return to the actual model. First you need to acquire the Expected Market Return, this will be used to calculate the projected market capitalization rate.

After you’ve acquired Expected Market Return, substitute the value into the calculation for Market Capitalization Rate. The Market Capitalization rate is given via the Capital Asset Pricing Model:

With the Market Capitalization Rate acquired, we can begin to calculate the actual value. Substitute the dividend value for the year, the Market Capitalization Rate, and the amount of the year into the equation below. Using the example above, if you were substituting for your first year, you would place 2.20 in the numerator, the market capitalization rate, and the number “1” for “Year” in the formula. If you were substituting for your third year, you would place 2.74 in the numerator, and the number “3” for “Year in the formula. You would repeat this for all years except your last year, and calculate the values for each year.

For the last year, you will use a variation of the formula above. This formula requires that you add the final year’s dividend value, in this example the fifth year’s dividend of 3.53, with the projected share price for the fifth year. In order to calculate the last year, you need to calculate the Final Year’s Price for the share, discounted to present. That task requires computing a few numbers that can be easily derived from the firm’s financial statements. The first number you need is the dividend payout. Locate the firm’s dividends paid and divide that number by the firm’s Net Income. Save this Net Income, you will need it after this equation.

You also need to determine the firm’s Return on Equity. To determine this divide Net Income by Shareholder’s Equity, which gives you the ROE.

Substitute the Return on Equity and the Dividend Payout into the following equation and solve. This formula will give you a growth rate, which will be subtracted from the market capitalization rate we calculated earlier using the Capital Asset Pricing Model.

Once you’ve calculated the growth rate, you can substitute the result into the denominator of the following equation. At the same time, substitute the market capitalization rate into the denominator and subtract. Substitute your calculated projection for your last year’s dividend and the growth rate in the last year into the numerator. Then solve the equation.

Once you have calculated the Final Year’s Price, substitute that value into the equation below. Add Final Year’s Price with the Final Year’s Dividend projected earlier. Substitute the market capitalization rate acquired from the Capital Asset Pricing Model equation, and substitute year number for your final year. In this example the final year was the 5^{th} year, so you would substitute the number 5 into the equation. Note that the final year price represents the dividend in perpetuity. It basically does the job of calculating the price value of all dividends beyond the 5^{th} year. You do not have to worry about calculating future values beyond this year. It simply handles that problem for you.

With this step, you have all the information you need to calculate the current price value of a share. Add the output for each year and the final year’s value together. This is the current price of your shares according to the Dividend Discount Model. Note that this model is only as good as the original assumptions used to calculate the dividend projections. If you use completely unrealistic or flawed assumptions to calculate your projections, you will get completely unrealistic and flawed prices.

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